The index of the middle element is 4.
The list (0, 1, 1, 2, 3, 5, 8, 13, 17), the binary search algorithm calls Binary Search (list, 0, 8, 3). The index of the middle element is 4. The binary search algorithm works by dividing a list into halves and looking at the value in the middle of the list. This is compared with the target value, and based on the comparison, one-half of the list is discarded as the search is continued in the other half. This is continued until the target value is found or it is clear that it is not on the list. In the given case, the list is (0, 1, 1, 2, 3, 5, 8, 13, 17), and the algorithm calls Binary Search(list, 0, 8, 3).
Here, the first parameter of the Binary Search function is the list, the second parameter is the lower index of the part of the list being searched, the third parameter is the upper index, and the fourth parameter is the value being searched. In the given case, the lower index is 0, the upper index is 8, and the value being searched is 3. The index of the middle element in the list is calculated as (0 + 8) / 2 = 4.
Therefore, the index of the middle element is 4.
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Lara opened a savings account 1 year ago. The account earns 11% interest, compounded
continuously. If the current balance is $7,000.00, how much did she deposit initially?
Round your answer to the nearest cent.
As a result, Lara made a $6,262.71 initial deposit into her savings account.
How long will it take for your money to double if the interest rate is 12% annually compounded?A credit card user who pays 12% interest (or any other loan type that charges compound interest) will double their debt in six years. The rule can also be applied to determine how long it takes for inflation to cause money's value to decrease by half.
To calculate the initial investment, we can apply the continuous compounding formula:
A = Pe(rt)
Where:
A = the current balance ($7,000.00)
P = the initial deposit (unknown)
r = the annual interest rate (11% or 0.11 as a decimal)
t = the time in years (1 year)
Plugging in these values, we get:
$7,000.00 = Pe(0.11 * 1)
A shorter version of the exponential expression:
$7,000.00 = Pe0.11
$7,000.00 = P * 1.1166 (rounded to 4 decimal places)
Dividing both sides by 1.1166:
P = $6,262.71 (rounded to the nearest cent)
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DNA on the Ocean Floor (adapted from Baldi book and cont'd from homework 4)- DNA occurs on the ocean floor (outside of living cells) where it plays an important role in nourishing seafloor life. A random sample of ocean floor specimens from 116 locations around the world gives mean sample DNA concentration Xbar=0.2781g/m2 and sample standard deviation s=0.1803g/m2. A healthy concentration of ocean floor DNA is considered to be around 0.31 g/m2.
a. Use the p-value approach to test if the floor specimens mean DNA concentration are different to the what is considered a healthy concentration. Use alpha = 0.05. Start by writing the null and alternative hypothesis. Make sure you write a conclusion regarding the question about the floor specimen's DNA concentration. (1pt)
b. What if the question was: test if the floor specimens mean DNA concentration were less than what is considered a healthy concentration? What would the p- value be? (0.5 pts)
c. Repeat the one-sided test from b. using the 95% confidence interval approach. What do you conclude?
All parts are define in the below points.
Define the term random sample?A random sample is a subset of a population in which each individual or element in the population has an equal chance of being selected. It is a sampling method used in statistics and research to minimize bias and increase the generalizability of the findings to the larger population.
a. Hypotheses: Null Hypothesis: The mean DNA concentration of the ocean floor specimens is not significantly different from the healthy concentration (µ = 0.31g/m2). Alternative Hypothesis: The mean DNA concentration of the ocean floor specimens is significantly different from the healthy concentration (µ ≠ 0.31g/m2). Using a two-tailed t-test with alpha = 0.05, we find a p-value of 0.0003, which is less than the significance level. Therefore, we reject the null hypothesis and conclude that the mean DNA concentration of the ocean floor specimens is significantly different from the healthy concentration.
b. We would perform a one-tailed t-test with the alternative hypothesis that the mean DNA concentration is less than 0.31g/m2 if the goal was to determine whether the mean DNA concentration of the floor specimens was lower than what is regarded as a healthy concentration. It would have a p-value of 0.00015.
c. Using the 95% confidence interval approach, we construct a one-sided confidence interval for the mean DNA concentration. If the lower bound of the confidence interval is less than 0.31g/m2, we can conclude that the mean DNA concentration is less than the healthy concentration. The 95% confidence interval for the mean is (0.2457g/m2, 0.3105g/m2), which does not include the healthy concentration of 0.31g/m2. Therefore, we can conclude that the mean DNA concentration of the ocean floor specimens is less than the healthy concentration.
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a). We discover a p-value of 0.0003 using a two-tailed t-test with alpha = 0.05, which is below the significance level.
b). Its p-value would be 0.00015.
c). The safe concentration of [tex]0.31g/m^2[/tex] is not included in the 95% confidence interval for the mean, which is [tex](0.2457g/m^2,\ 0.3105g/m^2)[/tex].
Define the term random sample?A random sample is a portion of a community in which every person or component has an equal chance of being chosen. In statistics and research, it is a sampling technique used to reduce bias and improve the generalizability of the results to a broader population.
A). An hypothesis is a The null hypothesis states that there is no discernible difference between the mean DNA concentration of the ocean bottom samples and the healthy concentration [tex](\mu=0.31g/m^2)[/tex]. Alternative Hypothesis: The mean DNA concentration of the ocean floor samples differs considerably from the healthy concentration [tex](\mu\neq 0.31g/m^2)[/tex] in a statistically significant way. We discover a p-value of 0.0003 using a two-tailed t-test with alpha = 0.05, which is below the significance level. We therefore reject the null hypothesis and come to the conclusion that the mean DNA concentration of the samples from the ocean bottom differs significantly from that of healthy individuals.
B). If the objective was to determine whether the mean DNA concentration of the floor specimens was lower than what is considered as a healthy concentration, we would conduct a one-tailed t-test with the alternative hypothesis that the mean DNA concentration is less than [tex]0.31g/m^2[/tex]. Its p-value would be 0.00015.
C). We create a one-sided confidence interval for the mean DNA concentration using the 95% confidence interval method. The mean DNA concentrationis less than the healthy concentration if the lower limit of the confidence interval is less than [tex]0.31g/m^2[/tex]. The safe concentration of [tex]0.31g/m^2[/tex] is not included in the 95% confidence interval for the mean, which is [tex](0.2457g/m^2,\ 0.3105g/m^2)[/tex]. As a result, we can say that the average DNA concentration of the samples from the ocean bottom is lower than the healthy concentration.
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Find the coordinates of the midpoint of the line segment with the endpoints J(−2, 3) and K(4, −1)
Answer:
jwjwi7svwisg, I have y2ywgeu
An object moves in the xy-plane so that its position at any time tis given by the parametric equations X(0 = ? _ 3/2+2andy (t) = Vt? + 16.What is the rate of change of ywith respect t0 when t = 3 1/90 1/15 3/5 5/2'
The given parametric equations are X(t) = -3/2 + 2t and y(t) = vt² + 16, the rate of change of y with respect to "t" when t = 3 is 6v
We have the parametric equations that are X(t) = -3/2 + 2t and y(t) = vt² + 16.
At time t, the rate of change of y with respect to t is given by the derivative of y with respect to t, that is dy/dt.
So, y(t) = vt² + 16
Differentiating with respect to t, we get
⇒ dy/dt = 2vt.
Now, t = 3 gives us,
y(3) = v(3)² + 16 ⇒ 9v + 16.
Therefore, the rate of change of y with respect to t at t = 3 is
dy/dt ⇒ 2vt ⇒ 2v(3) ⇒ 6v.
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Interpreting a Z score from a sample proportion. Suppose that you conduct a hypothesis test about a population proportion and calculate the Z score to be 0.47. Which of the following is the best interpretation of this value? For the problems which are not a good interpretation, indicate the statistical idea being described. 19 a. The probability is 0.47 that the null hypothesis is true. b. If the null hypothesis were true, the probability would be 0.47 of obtaining a sample proportion as far as observed from the hypothesized value of the population proportion. c. The sample proportion is 0.47 standard errors greater than the hypothesized value of the population proportion d. The sample proportion is equal to 0.47 times the standard error. e. The sample proportion is 0.47 away from the hypothesized value of the population. f. The sample proportion is 0.47
If the null hypothesis were correct, there would be a 0.47 percent chance of getting a sample proportion that deviates from the population proportion's hypothesised value
What is proportion?Proportion refers to the relationship between two quantities or numbers, indicating how they are related to each other in size or amount.
According to question:The best interpretation of a Z score of 0.47 for a sample proportion is:
b. If the null hypothesis were correct, there would be a 0.47 percent chance of getting a sample proportion that deviates from the population proportion's hypothesised value.
This interpretation is in line with the definition of a Z score, which is a measure of how many standard deviations a sample statistic (in this case, the sample proportion) is not what would be anticipated if the null hypothesis were true. A Z score of 0.47 means that the sample proportion is 0.47 standard deviations away from the expected value under the null hypothesis. Therefore, the interpretation that the probability of obtaining a sample proportion as far or farther than observed from the hypothesized value of the population proportion is 0.47, assuming the null hypothesis is true, is the most appropriate.
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for class three girls taking classes at a martial art school, there are 4 boys who are taking classes, if there are 236 boys taking classes, predict the number of girls taking classes at the school. what's the answer
There are 59 groups of 3 girls, or 177 girls in total, taking classes at the school.
What is ratio?A ratio is a means to indicate the relative sizes of two or more items for the purpose of comparison. It can be shown with a colon or as a fraction. Mathematicians employ ratios for a variety of purposes, including comparing numbers, scaling up or down, and resolving proportions. Moreover, ratios can be employed in other mathematical processes, simplified, and transformed to percentages or decimals.
Given that for every three girls there are 4 boys in class.
Thus, the proportion can be given as:
4x = 236
x = 59
Now, the proportion of girls are 3x.
3(59) = 177 girls.
Hence, there are 59 groups of 3 girls, or 177 girls in total, taking classes at the school.
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Three ballet dancers are positioned on stage. If Jaylen is 12 feet straight behind Britney and 5 feet directly left of Diana, how far is Britney from Diana?
Britney is 13 feet away from Diana as per Pythogorean theorem.
What is pythagorean theorem?The Pythagorean theorem is a fundamental concept in geometry that relates to the sides of a right triangle. It states that in any right triangle, the sum of the squares of the lengths of the two shorter sides (the "legs") is equal to the square of the length of the longest side (the "hypotenuse").
In the given question,
We can use the Pythagorean theorem to solve this problem.
If we consider Britney and Diana as the endpoints of the hypotenuse of a right triangle, we can use Jaylen's position as a reference to find the lengths of the other two sides.
From the problem, we know that Jaylen is 12 feet behind Britney, which means that the distance between their positions is 12 feet. We also know that Jaylen is 5 feet left of Diana, which means that the distance between their positions is 5 feet.
Let's label the distance we want to find as x.
Then we can set up the following equation:
x² = 12² + 5²
Simplifying this equation, we get:
x² = 144 + 25x² = 169
Taking the square root of both sides, we get:
x = 13
Therefore, Britney is 13 feet away from Diana.
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(8,-4) and (-1-2) to the nearest tenth
What is the slope in the equation y=2× + 3?
Answer:
Use the slope-intercept form to find the slope and y-intercept.
Slope: 2y-intercept: (0,3)
Step-by-step explanation:
Answer:
(0,3).
Step-by-step explanation:
for example, y=2x+3 tells us that the slope of the line is 2 and the y-intercept is at (0,3).
O is the centre of this circle.
What is the size of angle x?
Fully justify your answer.
Answer:
x = 94°
Step-by-step explanation:
ABCD is a cyclic quadrilateral , its 4 vertices lie on the circle.
the opposite angles of a cyclic quadrilateral sum to 180° , that is
x + 86° = 180° ( subtract 86° from both sides )
x = 94°
suppose that 27.5% of car engines will fail if they have not had routine maintenance in the past five years. if routine maintenance is given to 23 cars, what is the probability that exactly 10 will not have engine failure? round your answer to six decimal places.
The probability that exactly 10 out of 23 cars will not have engine failure is 0.007638.
Step-by-step explanation: First, calculate the probability of an engine failing in five years with no routine maintenance, which is 27.5%. This can be written as a decimal, 0.275.Next, calculate the probability of an engine not failing in five years with routine maintenance. This probability is 100%-27.5% = 72.5%, written as a decimal 0.725.
Now, using the Binomial Distribution formula (nCr), calculate the probability of exactly 10 engines not failing out of 23 cars, where n = 23, r = 10 and p = 0.725. The equation would be [tex](23C10)*(0.725^{10})*(0.275^{13}) = 0.0076379904[/tex]
Finally, round the result to 6 decimal places, giving an answer of 0.007638.
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mrs bosoga recieved a share of 15 boxes of nestle cremora from a stokvel during december 2022
The journal entry in the stokvel's ledger to record the distribution of the Nestle Cremora boxes to Mrs. Bosoga would be as follows:
The Journal EntryDate Account Debit Credit
Dec 2022 Nestle Cremora ZAR 3,750
Dec 2022 Mrs. Bosoga ZAR 3,750
The Nestle Cremora account is debited with ZAR 3,750, representing the cost of the 15 boxes of Nestle Cremora (15 boxes x ZAR 250 per box). The Mrs. Bosoga account is credited with the same amount, indicating that she has received the Nestle Cremora boxes.
The impact on the stokvel's balance sheet would be a decrease in the value of the Nestle Cremora inventory by ZAR 3,750, which would be reflected as a reduction in the stokvel's assets.
The impact on the income statement would be negligible, as the distribution of the Nestle Cremora boxes would not result in any income or expense for the stokvel.
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Mrs. Bosoga is a member of a stokvel, a savings club where members contribute money regularly and receive payouts periodically. During December 2022, Mrs. Bosoga received a share of 15 boxes of Nestle Cremora from the stokvel. The market value of each box of Nestle Cremora at the time was ZAR 250. The stokvel keeps track of its transactions using a ledger. What would be the journal entry in the stokvel's ledger to record the distribution of the Nestle Cremora boxes to Mrs. Bosoga? Also, what would be the impact on the stokvel's balance sheet and income statement?
The Jones family has two dogs whose ages add up to 15 and multiply to 44. How old is each dog?
As per the equations, the two dogs are either 11 years old and 4 years old, or 4 years old and 11 years old.
What is factoring?Factoring is the process of breaking down a mathematical expression or number into its component parts, which can then be multiplied together to give the original expression or number. In algebra, factoring is often used to simplify or solve equations.
What is an equation?An equation is a statement that shows the equality of two expressions, typically separated by an equals sign (=). The expressions on both sides of the equals sign are called the "left-hand side" and "right-hand side" of the equation.
In the given question,
Let's call the age of the first dog "x" and the age of the second dog "y". We know that their ages add up to 15, so we can write:
x + y = 15
We also know that their ages multiply to 44, so we can write:
x * y = 44
Now we have two equations with two unknowns, which we can solve simultaneously to find the values of x and y.
One way to do this is to use substitution. From the first equation, we can solve for one variable in terms of the other:
y = 15 - x
We can substitute this expression for y into the second equation:
x × (15 - x) = 44
Expanding the left side, we get:
15x - x^2 = 44
Rearranging and simplifying, we get a quadratic equation:
x^2 - 15x + 44 = 0
We can factor this equation as:
(x - 11)(x - 4) = 0
Using the zero product property, we know that this equation is true when either (x - 11) = 0 or (x - 4) = 0.
Therefore, the possible values of x are x = 11 and x = 4.If x = 11, then y = 15 - x = 4, which means that the ages of the two dogs are 11 and 4.
If x = 4, then y = 15 - x = 11, which means that the ages of the two dogs are 4 and 11.
Therefore, the two dogs are either 11 years old and 4 years old, or 4 years old and 11 years old.
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-2 (x - 5) plssss helppp
Answer:
-2x + 10
Step-by-step explanation:
-2(x - 5)
-2(x) -2(-5)
-2x + 10
Helping in the name of Jesus.
Write in Simplest Form pls (8a^3)^-4/3
The solution is, (a/2) ^4 or a^4/16 is in Simplest Form of (8a^3)^-4/3.
What is an exponent in math?An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
here , we have,
(8a^-3)^-4/3
split into two parts
8^ -4/3 * (a^-3)^-4/3
using the power to the power rule we can multiply the exponents
8^(-4/3) *a^(-3*-4/3)
8^ (-4/3) * a^(4)
replace 8 with 2^3
(2^3)^(-4/3) * a^(4)
using the power to the power rule we can multiply the exponents
2^(3*-4/3) * a^(4)
2 ^ (-4) * a^4
the negative exponent means it goes in the denominator if it is in the numerator
a^4/2^4
make a fraction
(a/2) ^4
or a^2/16
Hence, The solution is, (a/2) ^4 or a^4/16 is in Simplest Form of (8a^3)^-4/3.
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modeling real life find the height of the roller coaster using two different methods. round your answers to one decimal place.a roller coaster. a right triangle is formed by taking the length of the roller coaster, 283 feet as the hypotenuse. the height of the triangle measures x feet. the angle between the hypotenuse and the height of the triangle measures 45 degrees.
The height of the roller coaster is 199.9 feet.
According to the information provided,
There are two methods you can use to find the height of the roller coaster.
Method 1: Trigonometric ratios
To use this method, we can use the fact that the angle between the hypotenuse and the height of the triangle measures 45 degrees.
We can thus use the trigonometric ratio for the sine of 45 degrees, which is √(2)/2.
Setting up the equation, we have,
⇒ sin(45 degrees) = x/283
Solving for x, we get:
⇒ x = 283sin(45 degrees)
= 199.9 feet
Therefore,
The height of the roller coaster is 199.9 feet.
Method 2: Pythagorean theorem
To use this method,
we can use the fact that the length of the roller coaster, 283 feet, is the hypotenuse of the right triangle.
We can thus use the Pythagorean theorem to find the height of the triangle.
Setting up the equation, we have,
283² = x² + h²
where h is the height of the triangle.
Rearranging the equation, we get,
h = √(283² - x²)
Substituting x = 283/√(2) (since the angle between the hypotenuse and the height of the triangle measures 45 degrees), we get,
h = √(283² - (283/√(2))²)
= 199.9 feet
Therefore, using either method, we can say that the height of the roller coaster is 199.9 feet.
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12. In the accompanying diagram, DE || BC, DB = 6,
and AE = 8. If EC is three times AD, find AD.
B
6
D
A
8
E
C
Answer:
AD=4
Step-by-step explanation:
please mark as brainliest
determine the general solutions of the equation sinx=cos2x-1
[tex]x=30^o,270^o \ [0^0\leq x\leq 360^0][/tex]
Explanation:
We know,
[tex]cos2x=cos^2 \ x-sin^2 \ x=1-2sin^2 \ x[/tex]
So, let's solve the equation now,
[tex]sin \ x=cos2x=1-2 \ sin^2 \ x[/tex]
[tex]\longrightarrow \ 2 \sin^2 \ x+sin \ x-1=0[/tex]
[tex]\longrightarrow \ 2 \sin^2 \ x+2\sin x-sin \ x-1=0[/tex]
[tex]\longrightarrow \ 2\sin \ x(sin\ x+1)-1(sin \ x+1)=0[/tex]
[tex]\longrightarrow \ (2\sin \ x-1)(sin \ x+1)=0[/tex]
Now,
[tex]2\sin \ x-1=0[/tex]
[tex]\longrightarrow \ sin \ x=\dfrac{1}{2}[/tex]
[tex]\longrightarrow x=sin^{-1}(\dfrac{1}{2})[/tex]
[tex]\longrightarrow x=30^o[/tex]
And, [tex]sin \ x+1=0[/tex]
[tex]\longrightarrow x=sin^{-1}(-1)=270^o[/tex]
As we just need the general solutions, we should take only this two values as the general solutions.
Answer:
[tex]30^0,270^0[/tex]
That's it!
Two lines are plotted on the same coordinate plane. The first line passes through the points (-5, -5) and (-3, -3). The second line passes through the points (3, 1) and (4, 2). The two lines are best described as:
A. intersecting, not perpendicular
B. intersecting and perpendicular
C. parallel
D. no relationship
The slopes of the two line are equal. Hence, the two lines are parallel.
What is slope of a line?A line's slope is a gauge of the line's steepness. The ratio of the vertical change (change in y) to the horizontal change (change in x) between any two locations on the line is what is meant by this term. When a line moves from left to right, the slope might be positive, negative, zero, or undefined. When a line moves from left to right, the slope can be negative (when the line is vertical). The slope is determined using the following formula and is represented by the letter m:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are any two points on the line.
Given that, the first line passes through the points (-5, -5) and (-3, -3).
The slope is given by:
slope = (change in y) / (change in x)
slope = (-3 - (-5)) / (-3 - (-5)) = 1
The second line passes through the points (3, 1) and (4, 2).
slope = (2 - 1) / (4 - 3) = 1
The slopes of the two line are equal. Hence, the two lines are parallel.
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please help me
9-9÷9÷9-9÷9
Answer:
0
Step-by-step explanation:
0
Thank me...........
Suppose a random sample of 80 measurements is selected from a population with a mean of 65 and a variance of 300. Select the pair that is the mean and standard error of x. a) O [65, 2.236] b) O [65, 2.036] c) O [65, 2.436] d) O [80, 2.136] O [65, 1.936] f) None of the above
The pair that is the mean and standard error of x is [65, 2.236]. So, the correct option is a.
Suppose a random sample of 80 measurements is selected from a population with a mean of 65 and a variance of 300. We are required to select the pair that is the mean and standard error of x. The standard error of the mean (SEM) is calculated as follows :
$$SEM = \frac{\sigma}{\sqrt{n}}$$
Where σ is the standard deviation, and n is the number of observations or sample size.
Given that variance,
σ2 = 300
Therefore,
σ = √300 = 17.32.
Substituting the values in the formula, we have
$$SEM = \frac{\sigma}{\sqrt{n}} = \frac{17.32}{\sqrt{80}} = 1.9365$$
Therefore, the mean and standard error of x is [65, 1.936]. Option A is not the answer because the value of the standard error in that option is incorrect. Option B is not the answer because the value of the standard error in that option is incorrect. Option C is not the answer because the value of the standard error in that option is incorrect.
Option D is not the answer because the first value in that option is not the mean of x. Option E is incorrect because the value of the standard error is incorrect.
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the relation r is defined on z as follows: [ is an even number] prove that the relation is an equivalence relation. for full credit you must prove that the relation is reflexive, symmetric, and transitive using the formal definitions of those properties as shown in lectures. you must give your proof line-by-line, with each line a statement with its justification. you must show explicit, formal start and end statements for the overall proof and for the proof case for each property. you can use the canvas math editor or write your math statements in english. for example, the universal statement that is to be proved was written in the canvas math editor. in english it would be: for all integers m and n, m is related to n by the relation r if, and only if, the difference m minus n is an even number.
Let m and n be two arbitrary integers. We want to prove that the relation R is an equivalence relation, i.e. it is reflexive, symmetric, and transitive.
Reflexive: We must show that mRm for all m ∈ Z.
Since the difference of m and m is 0, which is an even number, we have mRm.
Therefore, the relation R is reflexive.
Symmetric: We must show that if mRn, then nRm.
Let mRn, i.e., the difference of m and n is an even number.
Then the difference of n and m is also an even number.
Therefore, nRm, and the relation R is symmetric.
Transitive: We must show that if mRn and nRp, then mRp.
Let mRn and nRp, i.e., the difference of m and n is an even number and the difference of n and p is also an even number.
The sum of the difference of m and n and the difference of n and p is the difference of m and p, which is an even number.
Therefore, mRp, and the relation R is transitive.
Since the relation R is reflexive, symmetric, and transitive, it is an equivalence relation.
Conclusion: The relation R is an equivalence relation.
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if two indistinguishable dice are rolled, what is the probability of the event {(3, 3), (2, 3), (1, 3)}? hint [see example 2.]
If two indistinguishable dice are rolled, what is the probability of the event {(3, 3), (2, 3), (1, 3)}The probability of the event {(3, 3), (2, 3), (1, 3)}
If two indistinguishable dice are rolled, it is 3/36 or 1/12.
Explanation: Indistinguishable dice are dice that appear identical to one another but do not have unique markings. As a result, indistinguishable dice will have the same number of faces, but the values on each face will be identical.
The total number of possible outcomes is 6 * 6 = 36 because there are six possible outcomes for each roll of a single die.
The probability of rolling the numbers (3, 3), (2, 3), or (1, 3) can be determined as follows: 3/36 or 1/12
For each die, there are six possible outcomes, so there are 6*6, or 36 possible outcomes for two dice.
Because (3, 3), (2, 3), and (1, 3) are the only possible ways to obtain a 3 on one of the dice and a 3, 2, or 1 on the other, the probability is 3/36 or 1/12.
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Solve the simultaneous equations below using substitution.
y=10x+6
2y+5x=17
Give your answers as integers or decimals.
Therefore, the solution to the system of equations is: x = 1/5 and y = 8.
What is equation?An equation is a mathematical statement that asserts the equality of two expressions. Equations contain variables, which are symbols that represent unknown or varying quantities, and constants, which are known values. The variables and constants are connected by mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation, and the resulting expression on both sides of the equation must have the same value. Equations are used to solve problems, find unknowns, and express relationships between quantities. Some common types of equations include linear equations, quadratic equations, polynomial equations, exponential equations, and trigonometric equations.
Here,
We have the following system of equations:
y = 10x + 6
2y + 5x = 17
Using substitution method, we can substitute the expression for y in the second equation with the expression for y in the first equation:
2(10x + 6) + 5x = 17
Simplifying:
20x + 12 + 5x = 17
25x = 5
x = 5/25 = 1/5
Now we can substitute this value of x into either of the two original equations to find the corresponding value of y. Using the first equation:
y = 10(1/5) + 6
y = 2 + 6
y = 8
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a fraction nonconforming control chart is to be established with a center line of 0.01 and two-sigma control limits. (a) how large should the sample size be if the lower control limit is to be nonzero? (b) how large should the sample size be if we wish the probability of detecting a shift to 0.04 to be 0.50?
a) Sample size if the lower control limit is to be nonzero: 50
b) Sample size if the probability of detecting a shift to 0.04 is to be 0.50: 100
a) How large should the sample size be if the lower control limit is to be nonzero?
n = (2σ / d)²We know that:
Center line (CL) = 0.01
Sigma (σ) = LCL = 0.005
d = Centerline - LCL = 0.01 - 0.005 = 0.005
Substituting the values in the formula, we get
n = (2 * 0.005 / 0.01)²= 50 Hence, if the lower control limit is to be nonzero, the sample size should be 50.
b) How large should the sample size be if we wish the probability of detecting a shift to 0.04 to be 0.50?
The probability of detecting a shift to 0.04 is denoted by β and is calculated using the following formula:
β = Φ [(-Zα/2 + Zβ) / √ (p₀q₀/n)], Where, Φ is the standard normal distribution function, Zα/2 is the critical value for the normal distribution at the (α/2)th percentile, Zβ is the critical value for the normal distribution at the βth percentile, p₀ is the assumed proportion of nonconforming items, q₀ is 1 – p₀, and n is the sample size.
In order to determine the sample size, we must first select a value for β. If we select a value for β of 0.50, then β = 0.50. This implies that we have a 50% chance of detecting a shift if one occurs. Since the exact value for p₀ is unknown, we assume that p₀ = 0.01, which is equal to the center line.
n = (Zα/2 + Zβ)² p₀q₀ / β², Substituting the values in the formula, we get,
n = (Zα/2 + Zβ)² p₀q₀ / β²= (1.96 + 0.674)² (0.01) (0.99) / 0.50²= 99.7 ≈ 100
Hence, if we wish the probability of detecting a shift to 0.04 to be 0.50, the sample size should be 100.
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statistical literacy (a) if we have a distribution of x values that is more or less mound-shaped and somewhat symmetric, what is the sample size needed to claim that the distribution of sample means x from random samples of that size is approximately normal? (b) if the original distribution of x values is known to be normal, do we need to make any restriction about sample size in order to claim that the distribution of sample means x taken from random samples of a given size is normal
It is important to be aware that the distribution of sample means x may not match the distribution of the original x values exactly, due to sampling variability.
then the sample size needs to be larger, possibly 50 or 30the sample size needed to claim that the distribution of sample means x from random samples of that size is approximately normal depends on the shape of the original distribution of x values. If the distribution is mound-shaped and somewhat symmetric, then the sample size needs to be fairly large, around 30 or more. However, if the original distribution of x values is strongly skewed or has outliers statisticl literacyif the original distribution of x values is known to be normalize size needs to be large, then the sample size does not need to be restricted in order to claim that the distribution of sample means x taken from random samples of a given size is normal. The sample size should still be at least 30, as this is necessary to produce a reliable result.
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Head Stevedore loads extra large boxes, also in the shape of perfect cubes. The volume of each box is 512 cubic feet
As per the volume, the dimension of an Extra Large Box is 3.78 feet.
Let's call the length of one side of the cube "s". Since the volume of the cube is given as 512 cubic feet, we can set up an equation to relate the volume to the length of one side:
Volume of cube = s³ = 512 cubic feet
To solve for "s", we can take the cube root of both sides of the equation:
s = ∛512
We can simplify this expression by finding the prime factorization of 512:
512 = 2⁹
Therefore, we can rewrite the expression for "s" as:
s = ∛2⁹
Using the properties of exponents, we know that the cube root of 2^9 is the same as 2 raised to the power of (1/3) times 9:
s = [tex]2^{1/3} \times 9^{1/3}[/tex]
We can simplify this expression further by recognizing that 9 is a perfect cube, and its cube root is 3:
s = [tex]2^{1/3} \times 3[/tex]
Therefore, the length of one side of the cube-shaped box is:
s = [tex]2^{1/3} \times 3[/tex] feet
Since all sides of the cube are equal in length, the dimensions of the box are:
Length = Width = Height = [tex]2^{1/3} \times 3[/tex] feet = 3.78 feet.
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Complete Question:
Head Stevedore loads Extra Large Boxes, also in the shape of perfect cubes. The volume of each box is 512 cubic feet. What are the dimension of an Extra Large Box?
At maxs party 3/12 of the guests are 10 year old and 7/12 of guests are 11 year old what fraction of the guests are 10 or 11 years old
The fraction of the guests are 10 or 11 years old is 5/6
A fraction represents a part of a whole, where the whole is divided into equal parts.
To find the fraction of guests who are 10 or 11 years old, we need to add the fractions of guests who are 10 years old and 11 years old.
3/12 of the guests are 10 years old, which can be simplified to 1/4.
7/12 of the guests are 11 years old.
Therefore, the fraction of guests who are 10 or 11 years old is
1/4 + 7/12 = 3/12 + 7/12
Add the fractions
= 10/12
Simplify the fraction
= 5/6
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Given the triangle, find the length of z. Give your answer in simpliest radical form.
three potential employees took an aptitude test. each person took a different version of the test. the scores are reported below. kaitlyn got a score of 74.5 ; this version has a mean of 68.5 and a standard deviation of 12 . kiersten got a score of 244.8 ; this version has a mean of 210 and a standard deviation of 29 . rebecca got a score of 7.24 ; this version has a mean of 6.7 and a standard deviation of 0.3 . if the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?
Step-by-step explanation:
kaitlyn score is 6 points above the mean
z-score = 6 / 12 = .5
kiersten score is 34.8 above the mean z-score = 34.8/29 = 1.2
rebecca score is .54 above the mean z -score = .54/ .3 = 1.8
rebecca scored the highest percentile (highes z-score) of the three....the best